Test the series sigman 1infinity 4nn for convergenceSolutio

Test the series sigma_n = 1^infinity (4^n/n!) for convergence

Solution

by series ratio test :

if Lt n->infinity   |an+1/an|<1 then series converges

checking

lt n-> infinity (4^(n+1)/(n+1)!)/(4^n n!)

=> |4/n+1|

=>0

hence converges